1. Translation: We can start by translating △ABC so that point A coincides with point G. Since corresponding parts of congruent triangles are in the same position, this translation will ensure that △ABC and △GHE have one pair of corresponding sides (side AG and side GH) that are congruent.
2. Rotation: After translating △ABC, we can rotate it clockwise or counterclockwise until line AB is aligned with line GH. This rotation will preserve congruency of corresponding angles, resulting in △ABC and △GHE having two pairs of corresponding angles that are congruent (angle B and angle E, and angle C and angle H).
3. Reflection: Finally, we can reflect △ABC over the line bisecting angle A, so that point B coincides with point E and point C coincides with point H. This reflection will ensure that the remaining pair of corresponding sides, side BC and side HE, are congruent.
After performing these three transformations, we have shown that △ABC is congruent to △GHE.
put that in easier words
We can make △ABC and △GHE congruent by following these steps:
1. Move △ABC so that point A is at the same position as point G. This ensures that side AG and side GH are congruent.
2. Rotate △ABC either clockwise or counterclockwise until line AB aligns with line GH. This makes angle B congruent to angle E and angle C congruent to angle H.
3. Reflect △ABC over the line that bisects angle A so that point B is at the same position as point E and point C is at the same position as point H. This ensures that side BC is congruent to side HE.
By doing these three actions, we prove that △ABC is congruent to △GHE.